The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.
The goal of seismic exploration is to obtain information (images) of the earth subsurface so one can identify hydrocarbon structures present below the earth surface without any expensive or time consuming drilling. The Earth is composed of different layers with different physical properties. The acquired seismic sample data contains reflections from these different layers. By analyzing these layers after obtaining an image of the subsurface, geologists can predict the likelihood of hydrocarbon existence.
Generally, the process of acquiring seismic data is governed by the Nyquist-Shannon theorem, and seismic data is captured by sampling a seismic signal at least two times faster than the signal bandwidth. If one is interested to increase the resolution, he/she has to increase the sampling rate (number of samples). Large amount of data is thus acquired based on the sampling, leading to significant cost of acquiring and processing of such large amount of data.
In order to bypass the Nyquist-Shannon theorem and reduce the amount of seismic data, there exists a new nonlinear sampling theory known as Compressive Sensing (CS). The seismic signals can be sparse in some particular domains, such as curvelet, Radon, wave atom, Fourier, and the like. Compressive sensing exploits the sparse structure of the seismic signals and enables recovery of a high resolution signal using a small number of measurements far less compared to samplings based on the Nyquist-Shannon theorem. The compressive sampling rate is bounded by the sparsity of the seismic data instead of the Nyquist rate.